The correct classification of astronomical objects -such as stars and galaxies -is essential to the field of astronomy. Today, however, with the advent of powerful next generation telescopes, the quantity of images being collected far exceeds the amount that can be catalogued by astronomers through their own observations and analyses alone. As just one example, the Large Synoptic Survey Telescope ("LSST"), opening in August 2024, will catalogue around 40 billion images of stars and galaxies. Certain machine learning models have proven efficient and accurate in classifying astronomical images. In this paper, we tested the ability of four different machine learning models to classify images of stars and galaxies accurately without inputs of additional measurements of the brightness, size, or shape of stars or galaxies: a convolutional neural network ("CNN") model, a logistic regression model, a random forest classifier, and a small neural network. We discuss and compare the architecture and performance of each model. We found that our neural network model trained on a data set preprocessed using a data preprocessing technique known as Principal Component Analysis ("PCA"), performed the best achieving an accuracy of 84 percent out of sample. We thus demonstrate that using such machine learning models can be an effective way to classify images of stars and galaxies, substantially reducing the time required to catalogue them.